Mia and Diego's stand is a hit. Now they must reason with ratios, unit rates, and percent to grow it wisely.
After a record weekend, the community center called with a request: 30 cups of the cousins' famous mango smoothie for a Saturday event. Diego's eyes went wide. "Thirty cups? We've never mixed that much at once. If we get the recipe wrong, we waste fruit โ and money."
Mia stayed calm. "We won't guess. Grandma's recipe is a fixed ratio: 2 parts mango to 3 parts yogurt. That's 5 parts in every batch. As long as we keep those parts proportional, the taste is guaranteed โ no matter how big the order."
2 parts mango + 3 parts yogurt = 5 parts total. For 30 cups: 30 รท 5 = 6 cups per part, so mango = 2 ร 6 = 12 cups and yogurt = 3 ร 6 = 18 cups.
Mia says they "won't guess." What does her reasoning show about why proportional thinking matters for a large order?
Using the 2:3 ratio, how many cups of mango are needed for the full 30-cup order? (Think in parts.)
To fill the order, the cousins needed mango in bulk. Three suppliers sent prices. Diego wanted the closest one; Mia wanted the smartest one. "Distance doesn't tell us the value," she said. "The unit rate does โ the price for one cup."
| Supplier | Mango | Price |
|---|---|---|
| Fresh Farms | 6 cups | $9.00 |
| Bulk Barn | 8 cups | $11.20 |
| Corner Mart | 5 cups | $7.75 |
Unit rate = price รท cups. Fresh Farms: $9.00 รท 6 = $1.50. Bulk Barn: $11.20 รท 8 = $1.40. Corner Mart: $7.75 รท 5 = $1.55.
"Bulk Barn is the better value," Mia concluded, "even though Corner Mart is closer. Lower unit rate, lower total cost."
Find Bulk Barn's unit rate: $11.20 for 8 cups. Cost per cup? (Type the dollar amount.)
Why does Mia choose Bulk Barn over the closer Corner Mart?
Now the big question: what to charge? Their cost worked out to $1.50 per finished cup. Diego suggested $3. "Is that fair?" he asked. Mia reached for percent. "A $3 price means $1.50 is cost and $1.50 is profit. The profit is half the price โ a 50% profit margin."
Profit margin = profit รท price = $1.50 รท $3.00 = 0.5 = 50%.
"And for the school discount," Mia added, "we take 20% off the $3 cup. 20% of $3 is $0.60, so students pay $2.40."
A cup sells for $3 and costs $1.50 to make. What percent of the price is profit? (Type the number only.)
Students get 20% off the $3 cup. What is the student price? (Type the dollar amount.)
The event was a triumph. Word spread, and a local league ordered 50 cups for a tournament. "If 10 cups bring in $30 at our regular price," Mia said, "we can scale that rate up for 50 cups." Diego set up the proportion and smiled at the result.
At the regular price, 10 cups earn $30. Using the same rate, how much do 50 cups earn? (Type the dollar amount.)
Across the whole story, how do ratios and unit rates serve different purposes for the cousins?
Choose one prompt. Write a clear paragraph (5โ7 sentences) that uses evidence (numbers) from the story.
Optional academic frame: "The evidence shows ______; therefore, ______. A trade-off is ______."
If the cousins keep a 50% profit margin but their cost rises to $2.00 per cup, what new selling price keeps that margin? Explain how you know. (Try it, then check with your teacher.)
| Category | 4 โ Advanced | 3 โ Proficient | 2 โ Developing |
|---|---|---|---|
| Comprehension & inference | All analysis questions correct; explains the author's reasoning | 2 of 3 correct | 1 correct |
| Multi-step math | All 5 Solve-It answers correct (part-to-whole, unit rate, percent, scaling) | 3โ4 correct | 2 correct |
| Mathematical argument | Clear claim supported by 2+ specific numbers; names a trade-off or connection | Claim with some evidence | States a claim with little evidence |
Grading accepts common formats (1.4, $1.40; 50, 50%; 150, $150).